Ch 22 - Neutron Stars & Black Holes

supermassive black hole

black hole having a mass a million to a billion times greater than the mass of the Sun; usually found in the central nucleus of a galaxy

neutron star

A dense ball of neutrons that remains at the core of a star after a supernova explosion has destroyed the rest of the star. Typical neutron stars are about 20 km across, and contain more mass than the Sun.

singularity

A point in the universe where the density of matter and the gravitational field are infinite, such as at the center of a black hole.

gravitational redshift

A prediction of Einstein's general theory of relativity. Photons lose energy as they escape the gravitational field of a massive object. Because a photon's energy is proportional to its frequency, a photon that loses energy suffers a decrease in frequency, which corresponds to an increase, or redshift, in wavelength.

time dilation

A prediction of the theory of relativity, closely related to the gravitational redshift. To an outside observer, a clock lowered into a strong gravitational field will appear to run slow.

millisecond pulsar

A pulsar whose period indicates that the neutron star is rotating nearly 1000 times each second. The most likely explanation for these rapid rotators is that the neutron star has been spun up by drawing in matter from a companion star.

Neutron Stars

After a type 1 supernova, little or nothing remains of the original star. After a type 2 supernova, part of the core may survive. it is very dense (as dense as an atomic nucleus) and is called a neutron star. Neutron stars although they have 1 - 3 solar masses, are so dense that they are very small. Important Properties: Rotation - as the parent star collapses, the neutron core spins very rapidly, conserving angular momentum. Typical periods are fractions of a second. Magnetic field - as a result of the collapse, the neutron star's magnetic field becomes enormously strong.

Observational Evidence for Black Holes

Black holes cannot be directly observed, as their gravitational fields will cause light to bend around them. The existence of black hole binary partners for ordinary stars can be inferred by the effect the holes have on the star's orbit or by ration from infalling matter. Cygnus x-1 -is a strong xray emitter thought to be a black hole, -its visible partner is about 25 solar masses -the system's total mass is about 35 solar masses, so the xray source must be about 10 solar masses -hot gas appears to be flowing from the visible star to an unseen companion -short-time scale variations indicate that the source must be very small. There are several other black-hole candidates as well, with similar characteristics. Their centers of many galaxies contain super massive black holes (about 1 million solar masses). Recently, evidence for intermediate-mass black holes has been found. These are about 100 - 1000 solar masses but origin is not well understood.

Neutron-Star Binaries

Bursts of xrays have been observed near the center of our galaxy. These have been thought to originate on neutron stars that have binary partners. The process is similar to a nova, but much more energy is emitted due to the extremely strong gravitational field of the neutron star. Most pulsars have periods between 0.03 and 0.3 seconds, but a new class of pulsar was discovered in early 1980s (millisecond pulsar). Millisecond pulsars are thought to be "spun-up" by matter falling in from a companion.

Tests of General Relativity

Deflection of starlight by the sun's gravity was measured during the solar eclipse of 1919; the results agreed with the predictions of general relativity. Another prediction - the orbit of Mercury should process due to general relativistic effects near Sun, again, the measurement agreed with this prediction

Do Black holes really exist

Evidence has been mounting but no direct observation of an event horizon, or first-hand measurement of black hole properties, has yet been made. So, probably, not definitely yet.

Gravitational Waves

General relativity predicts that orbiting objects should lose energy by emitting gravitational radiation. The amount of energy is tiny, and these waves are very difficult to detect. A neutron-star binary system has been observed (2 neutron stars); the orbits of the stars are glowing at just he rate predicted if gravity waves are carrying off the lost energy. The Laser Interferometric Gravity -wave Observatory (LIGO) was designed to detect gravitational waves (operating since 2003). It first observed gravitational waves from a merger of two black holes.

event horizon

Imaginary spherical surface surrounding a collapsing star, with radius equal to the Schwarzschild radius, within which no event can be seen, heard, or known about by an outside observer.

What's inside a black hole?

No one knows. Present theory predicts that the mass collapses until the radius is zero and its density is infinite, but it is unlikely that this actually happens. Need to learn more about what happens in such extreme conditions.

pulsar

Object that emits radiation in the form of rapid pulses with a characteristic pulse period and duration. Charged particles, accelerated by the magnetic field of a rapidly rotating neutron star, flow along the magnetic field lines, producing radiation that beams outward as the star spins on its axis.

gamma-ray burst

Object that radiates tremendous amounts of energy in the form of gamma rays, possibly due to the collision and merger of two neutron stars initially in orbit around one another.

neutron degeneracy pressure

Pressure due to the Pauli exclusion principle, arising when neutrons are forced to come into close contact.

Einstein's Theories of Relativity

Special Relativity: 1. The speed of light is the maximum possible speed, and it is always measured to have the same value by all observers. 2. There is no absolute frame of reference, and no absolute state of rest. 3. Space and time are not independent but are unified as spacetime. General relativity: It is impossible to tell from within a closed system whether one is in a gravitational field or accelerating. Matter tends to warp space-time, and in doing so redefines straight lines (the path a light beam would take). A black hole occurs when the "indentation" caused by the mass of the hole becomes infinitely deep.

Summary of Chapter 22

Supernova may leave behind a neutron star Neutron stars are very dense, spin rapidly and have intense magnetic fields. Neutron stars may appear as pulsars due to the lighthouse effect. A neutron star in a close binary may become an X-ray burster or a millisecond pulsar. Gamma-ray bursts are due either to 2 neutron stars colliding to hypernovas. If core remnant is more than about 3 solar masses, it collapses into black hole. We need general relativity to describe black holes; it describes gravity as the warping of space time. Anything entering within the event horizon of a black hole cannot escape. The distance from the event horizon to the singularity is called the Schwarzschild radius. A distant observer would see an object entering black hole subject to extreme gravitational redshift and time dilation. Material approaching a black hole will emit strong X-rays. A few such X-ray sources have been found and are black hole candidates.

Schwarzschild radius

The distance from the center of an object such that, if all the mass compressed within that region, the escape velocity would equal the speed of light. Once a stellar remnant collapses within this radius, light cannot escape and the object is no longer visible.

Space Travel near Black holes

The gravitational effects of a black hole are unnoticeable outside of a few Schwarzschild radii- black holes do no "suck in" material any more than an extended mass would. Matter encountering a black hole will experience enormous tidal forces that will both heat it enough to radiate and tear it apart. A probe nearing the event horizon of a black hole will be seen by observers as experiencing a dramatic redshift as it gets closer, so that the time appears to be going more and more slowly as it approaches the event horizon. This is called a gravitaitonal redshift - it is not due to motion, but to the large gravitational fields present. The probe, however, does not experience any such shifts; time would appear normal to anyone inside. A photon escaping fro the vicinity of a black hole will use up a lot of energy doing so; it cannot slow down, but its wavelength gets longer and longer.

lighthouse model

The leading explanation for pulsars. A small region of the neutron star, near one of the magnetic poles, emits a steady stream of radiation that sweeps past Earth each time the star rotates. The period of the pulses is the star's rotation period.

Black Holes

The mass of a neutron star can't exceed 3 solar masses. If a core remnant is more massive than that, nothing will stop its collapse, and it will become smaller and smaller and denser and denser. Eventually, the gravitational force is so intense that even light cannot escape. The remnant has become a black hole. The radius at which the escape speed form the black hole equals the speed of light is called the Schwarzchild radius. The Earth's Schwarzschild radius is about a cm; the Sun's is about 3 km. Once the black hole has collapsed, the Schwarzschild radius takes on another meaning, it is the event horizon. Nothing within he event horizon can escape the black hole.

equivalence principle

The principle that there is no experimental way to distinguish between a gravitational field and an accelerated frame of reference.

general theory of relativity

Theory proposed by Einstein to incorporate gravity into the framework of special relativity

x-ray burster

X-ray source that radiates thousands of times more energy than our Sun, in short bursts that last only a few seconds. A neutron star in a binary system accretes matter onto its surface until temperatures reach the level needed for hydrogen fusion to occur. The result is a sudden period of rapid nuclear burning and release of energy.

black hole

a region of space where the pull of gravity is so great that nothing - not even light - can escape. A possible outcome of the evolution of a very massive star.

Lorentz contraction

apparent contraction of an object in the direction in which it is moving

Pulsars

first pulsar was discovered in 1967. It emitted extraordinarily regular pulses; nothing like it had ever been seen before. After some initial confusion, it realized that this was a neutron star, spinning very rapidly. Why would a neutron star flash on and off? Lighthouse effect - strong jets of matter are emitted at the magnetic poles. If the rotation axis is not the same as the magnetic axis, the 2 beams will sweep out circular paths. If the Earth lies in one of those paths, we will see the star pulse. Pulsars radiate their energy away quite rapidly; the radiation weakens and stops in a few tens of millions of years, making the neutron star virtually undetectable. Pulsars also will not be visible on Earth if their jets are not pointing our way. There is a pulsar at the center of the Crab Nebula. The Crab Pulsars also pulses in the gamma-ray spectrum

Neutron-Star Binaries

in 1992, pulsar was discovered whose period had unexpected, but very regular variations. These variations were thought to be consistent with a planet, which must have been picked up by the neutron star, not the progenitor star.

Special Relativitity

late 19th century, Michelson & Morley did experiment to measure variation in speed of light with respect to the direction of the Earth's motion around the Sun. They found no variation - light always traveled at the same speed. This later became foundation of special relativity. taking the speed of light to be constant leads to some counter-intuitive effects - length contraction, time dilation, the relativity of simultanelty and the mass equivalent of energy.

spacetime

single entity combing space and time in special and general relativity

microquasar

stellar sized source of energetic X and gamma radiation, powered by accretion onto a neutron star or black hole, somewhat like a quasar but on a much smaller scale

remnant

the object left behind after a supernova explosion. Can refer to (1) the expanding and cooling shell of glowing gas resulting from the event, or (2) the neutron star or black hole that remains at the center of the explosion

special theory of relativity

theory proposed by Einstein to deal with the preferred status of the speed of light

Gamma-Ray Bursts

they occur and were first spotted by satellite looking for violations of nuclear test ban treaties. The gamma-ray bursts must originate from outside our galaxy. These are some sample luminosity curves for gamma-ray bursts. Note that some are very short, while others last much longer. Measurement of the spectrum of the visible afterglow of a gamma-ray burst allows its distance to be determined. Two models of source of gamma-ray burst - a) merging neutron stars OR b) a hypernova Both models are probably correct. The shorter bursts must come from a source no larger than about 300 km in diameter; these would be explained by neutron star mergers. The longer bursts may come from hypernova.